The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min).

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. To convert rpm into radians per second, I find it helpful to remember that rpm is revolutions per minute and writing it this way: rev's with a division sign 'per' and minutes on the bottom and then we can see that if we write 1 minute for every 60 seconds the minutes will cancel and we can multiply by 2π radians— one full circle, in other words— for every revolution and the revolution's cancel leaving us with radians per second. So 7200 times 2π divided by 60 gives 750 radians per second. The linear speed of a point directly underneath the reading head when it's positioned 3 centimeters from the center of the hard drive platter will be 3 times 10 to the minus 2 meters— converting that centimeters into meters— times by the angular velocity of the platter which is 753.98 radians per second and that gives linear speed of a point right under the reading head of 23 meters per second; notice how I use the unrounded number in the calculation to avoid intermediate rounding error. And then if there's a writing head positioned there and it can write 1 bit for every 0.5 micrometers where I have written 0.5 times 10 to the minus 6 meters here and then times that by the speed that the point underneath the writing head is going— linear speed, 22.619 meters per second— the meters cancel and we get 4.5 times 10 to the 7 bits per second.